The daily recommended intake of calcium for an average adult is 1,000 mg. There is 125 mg of calcium in 100 grams of milk. If a 150 g smoothie contains 75 grams of milk, how many grams of smoothie should an adult consume to meet the daily recommended intake?

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All right. Hi, everyone. So this question says that the daily recommended intake of calcium for an average adolescent is 1300 mg. There are 125 mg of calcium in 100 g of milk. If a 250 g smoothie contains 125 g of milk. How many grams of smoothie should an adolescent consume to meet the daily recommended intake? And here we have four different choices labeled A through D proposing different values in grams. So to answer this question, right, our task is to convert milligrams of calcium, 2 g of smoothie using a few different conversion factors given to us in the text of the question. First, there are 125 mg of calcium in 100 g of milk. And in addition to this 250 g of the smoothie contain 125 g of milk. Now, in this case, one of our conversion factors contains our starting units which are milligrams of calcium and the other contains our final units which are the grams of smoothie. So that corresponds to the order in which these conversion factors are going to be used. So because we're trying to make sure that the adolescent meets their daily calcium intake, that's recommended. Our first value should be 1300 milligrams of calcium. So using our first conversion factor, we're going to cancel out milligrams of calcium and find how many grams of milk are needed to meet the daily recommended intake. Now recall that when using conversion factors in dimensional analysis, the aim is always to cancel out your starting units. So if I treat my conversion factor like a fraction, the value of my conversion factor whose units are milligrams of calcium should go in the denominator. Whereas 100 g of milk should go in the numerator because by doing this, we ensure that milligrams of calcium cancel out. And our current answer is expressed in units of grams of milk. So using our second conversion factor, we can convert the grams of milk into the grams of the smoothie. So in our second conversion factor, grams of milk should go in the denominator because the idea is to cancel it out or cancel out those units. So our second conversion factor is 250 g of smoothie per 125 g of milk. And once again, grams of milk cancel out. So to evaluate this expression, our starting value that's 1300 gets multiplied by the numerators and divided by the denominators of the conversion factors. This gives us a final answer of 2080 g of the smoothie. Now here the daily recommended intake of calcium has two significant figures in its number. So our answer should reflect that this means that I can rewrite 2080 g of smoothie as 2.1 multiplied by 10 to the third power grams of smoothie and there you have it. So our final answer rounded to two significant figures is 2.1 multiplied by 10th of the third graphs. And this corresponds to option a in the multiple choice. So with that being said, thank you so very much for watching. And I hope you found this helpful.

The daily recommended intake of calcium for an average adult is 1,000 mg. There is 125 mg of calcium in 100 grams of milk. If a 150 g smoothie contains 75 grams of milk, how many grams of smoothie should an adult consume to meet the daily recommended intake?

Verified Solution

Key Concepts

Calcium Content Calculation

Proportional Relationships

Daily Recommended Intake